278 / 2019-09-27 16:32:19

Using BESO for hole nucleation in level set based topology optimization

hole nucleation; level set method; BESO; topology optimization; multi-material structures

结构优化与结构行为分析 > 结构优化与拓扑优化

Because the BESO takes discrete design parameterization (0 representing void and 1 representing solid material), when a small amount of inefficient material is removed from the interior of a structure, the effect is essentially the same as that of using the topological derivative to nucleate a hole. Therefore, a method is proposed to nucleate holes during the level based topology optimization by using the material removal scheme of the bi-directional evolutionary optimization (BESO). A strategy determining where and when to conduct generalized hole nucleation is presented.

Moreover, when a multi-material structure is optimized by using the level set method, besides the topological changes that are familiar to people (i.e., vanishing of a hole, nucleation of a hole, merging of holes, and breaking apart of a region), another topological change, i.e., the conversion between a pair of materials, is also possible to happen but receives little attention. In this case, a hole is no longer a region of void but becomes occupied by a different solid material. In our present study, such a topological change is called the generalized hole nucleation, and the material conversion scheme of the BESO is integrated into the level set based framework to deal with it.

As compared with the topological derivative, the BESO is more accessible to engineers because of its conceptual simplicity and easiness of numerical implementation. In other words, the material removal scheme of the BESO is used as a poor man’s topological derivative in our present study.

The results of several numerical examples prove that the proposed hole nucleation method is effective and efficient.